A basic conservative belief in the early 1960s was need for Balanced Budgets. And based on that they opposed JFKs tax cuts. Bob Novak reported this debate at the time and it’s described in his memoir. It wasn’t a conservative policy until Reagan adopted it during the 1980 campaign.
Likewise the idea that Kennedy was eager to get out of Vietnam is nonsense. He had just instigated a coup that got Diem assassinated, not what you do when you’re trying to extricate yourself from that mess
JFK changed his mind on many issues in a very short period of time—his Vietnam policy was all over the place.
Further adding to the confusion was a CIA under Allen Dulles that had a habit of “going rogue” from time to time—and had a tendency to “present a narrative” rather than “just the facts”.
There is some evidence (debatable, but some evidence) that JFK had his doubts about Vietnam policy by 1963—after he had fired Allen Dulles.